Math Mornings
Mathematics is patterns and logic, imagination and rigor. It is a way of seeing and a way of thinking.
Math Mornings is a series of public lectures aimed at bringing the joy and variety of mathematics to students and their families. Speakers from Yale and elsewhere will talk about aspects of mathematics that they find fascinating or useful. The talks will usually be accessible to students from 7th grade and up, although occasionally some familiarity with highschool subjects will be helpful.
Math Mornings lectures will take place on three Sundays each semester, at Davies Auditorium, 10 Hillhouse Avenue. Join us at 10:30am for snacks and math games and demonstrations – the talks begin at 11am.
Math Mornings is partially funded by grants from the National Science Foundation. It is part of Yale’s Science Outreach program. To find out more see http://onhsa.yale.edu/scienceoutreachhome [1]
Click here for the videos of previous lectures. [2] (or on individual links below)
Fall 2016 Schedule:
 Sun, October 16: Asher Auel (Yale): Wallpaper, platonic solids and symmetry. Video [3]
The Platonic solids—the tetrahedron, cube, octahedron, dodecahedron, and icosahedron—are some of the most beautiful and symmetric geometrical objects in 3dimensional space. Their mysteries started to be unraveled by the ancient Greeks and still fascinate us today. In 1872, the German geometer Felix Klein proposed the Erlangen program, which sought to unify the study of geometry through the study of symmetries. We will investigate instances, from crystals to wallpaper, when symmetry can lead to a more fruitful understanding of geometry and vice versa. Talk also by the Hepsa Ely Silliman Memorial Fund.
 Sun, November 6: Tarik Aougab (Brown): What’s the biggest number you can think of? Video [4]
For every number we can name there is a bigger one, so there must be a number bigger than the total number of atoms in the observable universe. And there must be some numbers that are so incredibly large, they have more digits than the total number of atoms. That means that there is not enough matter in the universe to write one of these humongous numbers digit by digit, even if we wrote small enough that each digit was the size of an atom! Do these huge numbers have names? How do we talk about them? Why would we even want to? In this lecture we’ll discuss how to think and talk about these kinds of numbers. Hopefully by the end, we’ll all have a deeper appreciation for just how many numbers are out there waiting for us.
 Sun, November 13: Jessi Cisewski (Yale Stats): Mapping the distant Universe: statistical methods for studying the cosmos. Video [5]
Light we observe from quasars has traveled through the intergalactic medium (IGM) to reach us, and leaves an imprint of some properties of the IGM on its spectrum. There is a particular imprint of which cosmologists are familiar, dubbed the Lymanalpha forest. From this imprint and with help from statistics, we can construct a map of the very distant Universe. I will introduce the special data that allow us to “see” deep into the cosmos and discuss the statistical framework that provides a way to fill in the gaps between our observations.
Fall 2015 Schedule:
 Sun, October 11: Stefan Steinerberger (Yale): Getting the most out of circles. Video [6]
If you have a loopy string, how would you arrange it to capture the most area? Already in ancient times people knew that it had to be the circle but if you think about it a bit more, it is not really quite so easy to see why that is the case. We will travel through all of history starting in the ancient kingdom of Carthage (with layovers in Switzerland, the animal kingdom and the realm of computer programs) and discover stepbystep why the circle is really the nicest shape there is.
 Sun, November 1: Kelly Delp (Cornell): What can you make using cellular automata?
Suppose we have a line of boxes, each with two possible states, black or white. A 1dimensional cellular automaton is a simple set of rules for determining how the states of these boxes change over time. Slight changes in the rules can lead to vastly different patterns. In this talk we will look at examples of these 1dimensional (and possibly 2dimensional) automata and see how mathematical artists use them in beadwork, knitting, and image processing.
 Sun, November 15: Sam Taylor (Yale): Flips, Slides, and Turns: Understanding the patterns found in nature, history, and art.
Patterns are all around us! From Persian tapestries and Egyptian tombs, to honeycombs in beehives, to the wallpaper in your living room, repeating patterns appear not only throughout art and history–they’re easy to find in our everyday lives. Come join in an interactive exploration of these repeating images, and learn how mathematics can be used to show how all the patterns that exist can be categorized into just 17 types.
Spring 2015 Schedule:
 Sun, February 8: Nathan Kaplan (Yale University): Points, Lines, Puzzles. Video [7]
TicTacToe is a game that is probably familiar to you from elementary school. Odds are that you don’t play much TicTacToe these days. There is a great observation from the great math puzzle guru Martin Gardner: “Many players have the mistaken impression that because they are unbeatable they have nothing more to learn.” If we change the rules of TicTacToe just a little bit we are led to interesting unsolved problems. For example, is there a winning strategy for X in the 5 x 5 x 5 version of TicTacToe?
We will introduce several other games and problems that have to do with points and lines. For example, it is known that we can choose 16 squares on an 8 x 8 chessboard so that no three squares lie on a line. But what happens with larger boards? Can we always pick 2n points from an n x n board with no three on a line? Can you find a way to place 9 points in the plane so that there are 10 different lines containing exactly 3 points? These problems may sound like they’re just for fun, but they are actually related to important questions at the cuttingedge of mathematical research!
 Sun, February 22: Michael Frame (Yale University): How to grow fractals.
Fractals are shapes that look a lot like themselves when you magnify every little piece of them. We’ll see some examples of fractals in the natural world, and inside ourselves. These shapes seem complicated, but can be really simple if we focus on how they grow instead of how they look. Mostly, we’ll learn how to recognize the pieces that make up a fractal, and how to find the rules to grow that fractal. Halfway through, you’ll understand what it means to turn a picture of a cat into a Sierpinski gasket. You’ll also hear one or two stories about Benoit Mandelbrot, whose trusty sidekick I was for 20 years.
Fall 2014 Schedule:

Sun, Nov 23: Yair Minsky (Yale University): The Many Faces of Euler’s Formula.
In 1750 Euler described a simple relationship among the numbers of vertices, edges and faces of a polyhedron. This wonderful formula has many implications and generalizations. Join us on a guided tour of Euler’s formula and and what it means for many parts of mathematics, from topographical maps to fluid flows, from geometry and symmetry to dynamical systems.
 Sun, Oct 19: Raphael Coifman (Yale University): Networks and Mathematics. Video [8]
This is an elementary talk to illustrate the remarkable organizational powers of random walks on Networks. It will not require any prior knowledge beyond middle school math.
We’ll describe a range of examples of Networks and their ubiquity in our life, from social networks to information , economic, political, weather and communication networks. Usually such networks can be organized as mathematical graphs, on which certain transitions,or transactions, or exposures are being quantified. We’ll see that a network based computational geometric approach for the sorting and organization of data and information leads to insights, understanding and predictions for complex systems. As specific examples we’ll describe the network of characters in a body of literature, the network of Congress, a network of romantic relations in a High School, and many others.

Sun, Oct 12: Roger Howe (Yale University): A dozen things about the number 12. video [9]
Spring 2014 schedule:
 Sun, Feb 23: Alex Kontorovich (Yale University): A mathematical duel: Cardano vs. Tartaglia and the cubic equation
 Sun, Feb 30: Andrew Granville (Universite de Montreal): Primes [10]. Video [11]
Fall 2013 schedule:

Sun, Sept. 29: Richard Schwartz (Brown University): Higher Dimensional Space and the Things in It. Video [12]
I will give a friendly introduction to higher dimensional space and talk about some of the objects in it, like spheres, cubes, and other polyhedra. I’ll explain some of the really weird properties of polyhedra in high dimensional space, and even convince you that these things are really true.
 Sun, Nov 10: Yair Minsky (Yale University): Infinity. Video [13]
How many guests can come into an infinite hotel? How many ping pong balls fit into an infinite barrel? What is 1/0? What is infinity minus infinity? Is 1 = 0.999999999…..? Can anything be infinitely large or infinitely small? Are there different sizes of infinity? In a finite world, why should we even care about this?
Come find out about these and infinitely many other questions on Sunday Morning, Nov 10.
 Sun, Nov 17: Amanda Folsom (Yale University): Patterns and Fractals in Numbers. Video [14]
There are five ways to break down the number 4 as a sum of positive whole numbers:
4 = 3 + 1 = 2+2 = 2 + 1 + 1 = 1 + 1 + 1 + 1
so we say there are five “partitions” of 4. This looks easy, right? Not so fast! Can you write down or count the partitions of 10? 100? 1000? Can you see any patterns? In this talk we’ll see how this seemingly easy business of adding and counting has led to some very beautiful and very difficult problems and ideas in mathematics and number theory. Come find out how “1 + 1 = 2” has fascinated mathematicians for centuries.
In 201213, our speakers were:
 Yair Minsky: Topology: The Shapes of Space & Spaces of Shapes. Video [15]
 George Hart: A Challenging Geometric Construction Video [16]
 Alex Kontorovich: The Riemann Hypothesis: How to make $1 million without getting out of bed. Video [17]
 Sam Payne: The Method of Archimedes Video [18]
 Michael Wolf: How Nature Chooses its Shape: The Mathematics of Soap Films Video [19]
 Asaf Hadari: Reflections on the Game of Billiards Video [20]